Precalculus
The bridge from algebra to calculus. By the end you'll see every standard function — polynomial, rational, exponential, trig — as a tunable, transformable, composable object, and you'll have your first informal encounter with the idea of a limit.
Function Transformations
Shifts, stretches, and reflections of y = f(x). The counter-intuitive horizontal cases and why order of composition matters.
Combining Functions
Arithmetic combinations and composition f ∘ g. Domain rules, why f ∘ g ≠ g ∘ f, and decomposing complicated functions into chains.
Inverse Functions
When a function is invertible (the horizontal line test), the swap-and-solve recipe, and the geometric meaning — reflection across y = x.
Polynomial & Rational Functions
End behavior, zeros and multiplicities, asymptotes, and holes. Sketching a polynomial and a rational function from scratch.
Limits — Introduction
The intuitive idea before the ε–δ formalism. Numerical tables, one-sided limits, 0/0 indeterminate forms, and limits at infinity.